CUET Mathematics - The solution of the differential equation (x^2 + xy)dy = (x^2 + y^2)dx is | PYQs + Solutions

CUET Mathematics 2025 27 May Shift 1

Calculus

Medium

core

$y + \log_e\left|\frac{y-2}{x}\right| = c$ , ( $c$ is an arbitrary constant)

$\frac{y}{x} + \log_e\left|\frac{(y-x)^2}{x}\right| = c$ , ( $c$ is an arbitrary constant)

$y - \log_e\left|\frac{y-x}{x}\right| = c$ , ( $c$ is an arbitrary constant)

$y^3 + \log_e\left|\frac{(y-x)^2}{x}\right| = c$ , ( $c$ is an arbitrary constant)

✅ Correct Option: 2

Related questions:

14 May Shift 2

For the differential equation $(x + y)dy + (x - y)dx = 0$ , which of the following is/are correct?

(A) Differential equation is homogeneous

(B) Order of differential equation is 1

(D) Degree of the equation is not defined

Choose the correct answer from the options given below:

14 May Shift 1

Consider the differential equation, $x\frac{dy}{dx} = y(log_e y - log_e x + 1)$ , then which of the following are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(D) Its general solution is $log_e\left(\frac{x}{y}\right) = Cy$ , where C is constant of integration

(E) If $y(1) = 1$ , then its particular solution is $y = x$

Choose the correct answer from the options given below:

16 May Shift 1

The particular solution of the differential equation x(1 + y²)dx - y(1 + x²)dy = 0, y(0) = 1, is:

CUET Mathematics 2025 27 May Shift 1 PYQs